From cab07447b590e734567ba6e33db14ea187ef5873 Mon Sep 17 00:00:00 2001 From: JGonzalez Date: Fri, 16 Dec 2022 19:27:10 +0100 Subject: [PATCH] Averge scheme documented Documentation of the average scheme for species properties. --- doc/user-manual/bibliography.bib | 11 +++++++++++ doc/user-manual/fpakc_UserManual.pdf | Bin 174638 -> 181016 bytes doc/user-manual/fpakc_UserManual.tex | 28 +++++++++++++++++++++++++-- 3 files changed, 37 insertions(+), 2 deletions(-) diff --git a/doc/user-manual/bibliography.bib b/doc/user-manual/bibliography.bib index 0ef1811..878b7ee 100644 --- a/doc/user-manual/bibliography.bib +++ b/doc/user-manual/bibliography.bib @@ -51,4 +51,15 @@ howpublished = {\url{https://gmsh.info/}}, } +@Article{welford1962note, + author = {Welford, BP}, + journal = {Technometrics}, + title = {Note on a method for calculating corrected sums of squares and products}, + year = {1962}, + number = {3}, + pages = {419--420}, + volume = {4}, + publisher = {Taylor \& Francis}, +} + @Comment{jabref-meta: databaseType:bibtex;} diff --git a/doc/user-manual/fpakc_UserManual.pdf b/doc/user-manual/fpakc_UserManual.pdf index a84376fbfd25742aa1fd9c11953d8d7b7b8171ca..66aba8b627f80119f5f78f25fd22176c034d96bb 100644 GIT binary patch delta 125670 zcmZs?Q*@@!w)P#nW7~G}#I|kQcG5|n*h$B>ZQHh!j@>aj*7slg-D`jE*y|mm4(?G0 z^PW`)SIzp(t7@0w(!=26+t4_OnTZ`uY~c9#nB>eIEZwY#0ZGUO6u=QJS;yZJ$h{Am zw^EoZ9+sX@?hHB*F!7?aSp4Yx#g)fksawP1Xw7}SyVHymD#<3qXU+2ER-G_f3hG%mDO;7YiT9%>>loucAxA{VAb9hbr@b|Z%%QqW)8 zF5omds#*e(WK_|f5Nd>$g-%BiIiIJAuqjgS1qd)wnXoY{0@k-tdIM;hsCz}6y?ja{ z2xZo&#YUU}MkNSP?Ge;uUj_)P)H&1w8I`d?6L+{IkZAfN2Kykt&E}XNlG?B3jC@;0 z+VdS`hC@W8aD}(wuzc?~vQ)S;izF}Vc77&a-SvK($Qo_Z?At5px|4?0wj3LXg7qBy0HJPAw z|NTRm7JkD_;=l-oYN`|Opxv?>jxVip z!8OV(ZmXR%M)%mNzw+ltZHol-9Ba39vUroz%G3P^G0-^LCv$jf(OSV-yh@6iYVZRC z_1gn0M0Wg_4o;fQQHN%=VLq)y5*@YGFEgfMvzrVKyoP=%T3u`qhwv z4DOA)RkJ7dafcLQ4!4pS<216uO{FLWZV6XLlx0YeFscR5d6$%&hTMNeTSRjAJ;uZ5 zl!L9gN?I3M%%l||a1;N@xwgn<6(r@5|BVSmeN#&yT%v#_X@=~_pxcLrOxdE&w2N6G zU$*Z0E)7QaX#Q zK%$~)7)W=JMG7jULhp%juNmj4XYqXq4X^HmbXnsQ$U%rA-;w_V}{Zu$ZT zc?$V=O#K(xVe4rd7R@}XTggq`-4tcf!=gxVZm{<&K}$>#99QA==H=`Eb|!K3Lsi%vi7 z{Mokp=O9)Tef=**dAE@MzFpdOv)XT(H4+u7G{sYS6&t;@V>9z1TRk7g^7nUOflA>H zx!Wv(4O&``T9jZ{)fa4SSL77kmM^$xZ1aeG>DzRVUV^BNF@Cr^v3PDH0l)8Wxy}i5jw!qDwAy6}{Rtb;jM$ilc1dRvz>%Kg z6+%W#yf7t_bCHI!oXHrEnT36TvqMV}O)c&2Kfd*rys$aj-(JPU9cG?H>b+I0ed7?5pySp3xfoe{e@7;F0U}3BRHbj#f*2GCMf!wXb(-?E9OD!({!< zaKm?|@C3spVPWS2z?nOk{Y&>bIRE1S;NVI^ zDIf>ZsWH#9sWF2HQ|Dw)L7vcJ)0(+rxZsFzLn%o^mLW5K60^xd%JR#yk+GqL#(C>(yHQAd}Zu<%gFAS4~<+W@21Jt`#DN02x}qMEK{|u5K>o#`gb{ z1lNBj!Oi;bDNc02eB}bJwW0JjeUN!&b0Z6L?u@OQQ+cQ#NVX=5(n6bS zs$eVI@{^X`-)yI2;mXGA-2}x*Dg4P_h+hH^*j;0C6TL}O=~o#Q9NKMj#M%~2tM_g4 z>I>K>a(QujJ)Sx66y$CbW61Wb@Ahs9*ndY%TZJr0<#faXI`-OV5~Bk*_pt zuc=Oz%|*DX6Ab?29F|t^Gyz~juFn$ba0`TvT2NvO)TN_V^*zwHf6;^_FUd-iXI{!m z%+1;?d#}jx$#cW}8`5`lTU(347`YDCpj46}prRk@km|?SMnL2bASpW@Q;sJ7jBR1J zN~#(dJCJyVn4kiEHs(>^^D5^`?EvJ(LKI11*Z5gbBFc7=c&<#0nBwep*kU}ds{T-D zC*gI_e!42;RS>9vxp#`mr>|r8g$H^g<`mW}P@#)P?*^rW@;0$bRWoZpVlgD8%0Wd` z$WL)5x(9KwV_dQpLxIu0|3`iUZaSHZ$#||{SV3?R+XdSl2}aKU==rb3Jx0mjqor!8 z-+1Oce1$NC<2`b{N6{MaKGWsFafL2XdRHe*8EF+0ysf~a@UQ4?^BZqGDq9g|oA!%w z-{pJu*CTy-#U-(uO@%5Q7l7k|uRV+gP9`sBjEpx*Kc`@`bF!4+S9IZ|RHxMp`#hx# zh@8|m*PrXA7DO3Y+f0TrZ`WIykl4ym^_E^KqubxbMuewr zIjGEug*Lzw`mdi+b=XmkvH=EchdiAX5nD&SQJ(5*?D87~1hM=KV%(X(r-U$md{4RY zbG2O$fC)s(4lC9)see?nxKRwoiDD4zHqW4+lzky9ThYfxh8w8T1InKmp$?tbE?~#z zo~eJts|hSS$BOs^s3;g!)?s`N(O!7wKkfG}AU=SO;}h&0*m?VJj24I8N}x~W?(9dJ zI1b!iJ|;^7d8o56N3Q84K;^+WaBs)ZG5hJPkk`J}-e`zvL_xD0b6m<7&jOGRc!Bj3 zN97O?zOwo1BmnVG;mi0lR!3S+eDn?2d8xbKZqKda=sE@0SFvCrG|Tnq<2@9Oi@yo_ zUVVX*5nF7_8=ZdsN*$=iW5#0BXlM2k>jZ%!VvGT%vkl(Q?R%gtLZ@TPIZZFb z5v_NNN#+H=QpoZy%opmnkenkdDz4MjB1L|Lg^9zrMRMDY7W&}aC-B$>3JS{UN7lbB zgW`l3+R(vrX7dvilKm{bNDl`)hBV_YMEC|KsL6!0R%qz^Fk3YBnOIj3*9E#sh&DyS z3c-l*ECDy9|Ga;^-X70bx z8B!~@uAE*dA{TpY4o6;EjC)}C)@gYA{-AvKI^k(EdjG?$KswJN1(ZlFDuxxU1=T&* z(WZOSLO?eW9{CC1|FW7y6|wZ5Q2kn5szsm3^n6@8=vIjd^Ma=nmo=sZtpey|*S?Io zH1;R5sEri4s4;RtjcAn7mKy6YR4#ffWol=5mDNu3 zD6HBlda^1^hIOrW+xAN7eM@y0LB# z8+oZK?&HOa!o$fupkWEe0DHJO*XI(?@7U8{WnJ)qOt6>!Ec~mzA=2_+#3+V*_mQc0R)Hu z!QVslReH4gEX}ldSai;z?O(0J!bG%lIiik*QW(UJScMALfo_Xm=FO(pMa`pc5P7F<5Ccs~&D

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zS9E}aSX-vSwfym2!; zC(2gfT;q}f>Tb@1NW|Rc1J`i3H^>;KL2MSnxsu&La0g&z&&RmSPe0gyVhYAN)Ed&mY)47z=+VpE1DAZkZ~o{1)lgoTrlv)t Yq-CT;$9RA)8rN|iZQAr4(97fh0Pc^)TmS$7 diff --git a/doc/user-manual/fpakc_UserManual.tex b/doc/user-manual/fpakc_UserManual.tex index b41f809..e5c0d4f 100644 --- a/doc/user-manual/fpakc_UserManual.tex +++ b/doc/user-manual/fpakc_UserManual.tex @@ -1,4 +1,4 @@ -\documentclass[10pt,a4paper,oneside]{book} +\documentclass[10pt,a4paper,twoside]{book} \usepackage[latin1]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} @@ -22,6 +22,7 @@ Author = {Jorge Gonzalez} } } +\usepackage[margin=1in]{geometry} % Reduces margins of the document % Allows breaking of URL in bibliography. \setcounter{biburllcpenalty}{7000} \setcounter{biburlucpenalty}{8000} @@ -260,6 +261,18 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Electromagnetic field} WIP. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Average scheme} + Particle-in-cell codes has an intrinsic statistical noise associated with them. + Although this can be reduced by increasing the number of particles, this also increases the CPU requirements of the case. + + It is quite common that most cases reach a quasi-steady state after a number of iterations and time-average results can be obtained after to improve analysis, plotting and restarting the case using these time-average results as new species backgrounds. + Although this is possible to do once the simulation is finished with post-processing tools, this is limited to the amount of iterations printed. + + \Gls{fpakc} implements a simple average scheme that, after a start time provided by the user, scores a mean and standard deviation of all the main species properties, and the electromagnetic field. + This scheme is based on the Welford's online algorithm~\cite{welford1962note}. + The averaged data is written in the same format as the input mesh at the end of the simulation. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Installation} @@ -642,7 +655,7 @@ make \item \textbf{initialTime}: Real. Units of $\unit{s}$. Initial simulation time. - If no value is provided, the initial time is set to $\unit[0]{s}$. + If no value is provided, the initial time is set to $\unit[0.0]{s}$. \item \textbf{pusher}: Character. Array dimension 'number of species'. Indicates the type of pusher used for each species: @@ -684,6 +697,17 @@ make File must be located at \textbf{output.path}. \end{itemize} \end{itemize} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \subsection{average} + This object determines the use of an average scheme. + If this object exists in the input file, average will be written at the end of the simulation. + Acceptable values are: + \begin{itemize} + \item \textbf{startTime}: Real. + Units in $\unit{s}$. + Simulation physical time in which average scheme will start to compute the mean and standard validation. + If no value is provided, the initial time is set to $\unit[0.0]{s}$. + \end{itemize} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{interactions}\label{ssec:input_interactions} This object determine the different interactions among species.